Simulating the thermal behavior of materials with discontinuities is a challenge in computational mechanics. This study proposes a nonlocal methodology for heat conduction analysis. The method evaluates temperature gradients by employing a nonlocal gradient operator. Using the temperatures of neighboring nodes, the temperature field within the surrounding area is approximated as a third-order polynomial. To ensure accuracy even with changing node positions, the gradient is corrected using Taylor series expansions and information from the previous time step. The proposed operator is validated through various problems with analytical solutions, including simple polynomials, temperature with sharp gradients, and oscillating fields. Complex geometries containing cracks are also analyzed and compared with the finite element method and Peridynamics, which is widely used for fracture analysis [1]. The results show good agreement with analytical solutions and effectively capture thermal responses in fractured materials. This approach is applicable to the thermomechanical analysis of construction materials under thermal shock or freeze-thaw cycles.